Real-time large-deformation substructuring

Figure 1: Examples produced by our data-driven finite element method. Left: A bar with heterogeneous material arrangement is simulated 15x faster than its high-resolution counterpart. Left-Center: Our fast coarsening algorithm dramatically accelerates designing this shoe sole (up to 43x). Right-Center: A comparison to 3D printed results. Right: We repair a flimsy bridge by adding a supporting arch (8.1x) speed-up. We show a High-Res Simulation for comparison. AbstractCrafting the behavior of a deformable object is difficult-whether it is a biomechanically accurate character model or a new multimaterial 3D printable design. Getting it right requires constant iteration, performed either manually or driven by an automated system. Unfortunately, previous algorithms for accelerating three-dimensional finite element analysis of elastic objects suffer from expensive precomputation stages that rely on a priori knowledge of the object's geometry and material composition. In this paper we introduce Data-Driven Finite Elements as a solution to this problem. Given a material palette, our method constructs a metamaterial library which is reusable for subsequent simulations, regardless of object geometry and/or material composition. At runtime, we perform fast coarsening of a simulation mesh using a simple table lookup to select the appropriate metamaterial model for the coarsened elements. When the object's material distribution or geometry changes, we do not need to update the metamaterial library-we simply need to update the metamaterial assignments to the coarsened elements. An important advantage of our approach is that it is applicable to non-linear material models. This is important for designing objects that undergo finite deformation (such as those produced by multimaterial 3D printing). Our method yields speed gains of up to two orders of magnitude while maintaining good accuracy. We demonstrate the effectiveness of the method on both virtual and 3D printed examples in order to show its utility as a tool for deformable object design.

Section: Related Workmentioning

confidence: 99%

Data-driven finite elements for geometry and material design

Chen¹,

Levin

Sueda

et al. 2015

“…Domain Decomposition: As is common in articulated subspace simulations [Yang et al 2013;Barbič and Zhao 2011;Kim and James 2011], we will assume that the mesh has been partitioned into subdomains. We used a simple nearest-neighbor strategy to associate each tet with the nearest bone, but our algorithm is agnostic to the partitioning method, so other methods could be used.…”

Section: Simulation Preliminariesmentioning

confidence: 99%

“…a forearm) is still fairly low-rank. Articulated subspace methods [Kry et al 2002;Kim and Pollard 2011], which include substructuring and domain decomposition approaches [Barbič and Zhao 2011;Kim and James 2011;Yang et al 2013] have thus been developed that successfully leverage this coherence.…”

Section: Introductionmentioning

confidence: 99%

Simulating articulated subspace self-contact

Teng

Otaduy²,

Kim

2014

Figure 1: A hand mesh composed of 458K tetrahedra, running at 5.8 FPS (171 ms), including both self-contact detection and resolution. Our algorithm accelerates the computation of complex self-contacts by a factor of 5× to 52× over other subspace methods and 166× to 391× over full-rank simulations. Our self-contact computation never dominates the total time, and takes up at most 46% of a single frame. AbstractWe present an efficient new subspace method for simulating the self-contact of articulated deformable bodies, such as characters. Self-contact is highly structured in this setting, as the limited space of possible articulations produces a predictable set of coherent collisions. Subspace methods can leverage this coherence, and have been used in the past to accelerate the collision detection stage of contact simulation. We show that these methods can be used to accelerate the entire contact computation, and allow self-contact to be resolved without looking at all of the contact points. Our analysis of the problem yields a broader insight into the types of nonlinearities that subspace methods can efficiently approximate, and leads us to design a pose-space cubature scheme. Our algorithm accelerates self-contact by up to an order of magnitude over other subspace simulations, and accelerates the overall simulation by two orders of magnitude over full-rank simulations. We demonstrate the simulation of high resolution (100K -400K elements) meshes in self-contact at interactive rates (5.8 -50 FPS).

“…Such simulations can be accelerated by orders of magnitude using model reduction, which makes it possible to timestep complex plants at interactive rates. Recently, the combination of domain decomposition and model reduction has received significant attention in the literature [Barbič and Zhao 2011;Kim and James 2011;Yang et al 2013]. Barbič and Zhao [2011] employed gradients of rotation matrices computed using polar decomposition, for structures without loops in the domain graph.…”

Section: Related Workmentioning

confidence: 99%

“…In a manner of minutes and with minimal user intervention, our system can pre-process virtually any plant, which we then simulate in an efficient domain decomposition simulator, accelerated using model reduction [Barbič and Zhao 2011]. Such a combination of authoring and fast simulation enables us to produce quality large-deformation dynamics of complex plants, under any given external forces, such as impulsive forces, gravity or wind.…”

Section: Introductionmentioning

confidence: 99%

Interactive authoring of simulation-ready plants

Zhao

Barbič

2013

Self Cite

Figure 1: Simulation of a peach tree with anatomically realistic geometry (Prunus Persica), with fracture. Peaches fall from the tree swaying in the space-time Perlin wind. 299,707 triangles, 237 branches, 3,556 twigs, 18,536 leaves, 330 fruits, 2,950 reduced DOFs, 7 hierarchy levels, 5 msec of simulation per graphical frame. AbstractPhysically based simulation can produce quality motion of plants, but requires an authoring stage to convert plant "polygon soup" triangle meshes to a format suitable for physically based simulation. We give a system that can author complex simulation-ready plants in a manner of minutes. Our system decomposes the plant geometry, establishes a hierarchy, builds and connects simulation meshes, and detects instances. It scales to anatomically realistic geometry of adult plants, is robust to non-manifold input geometry, gaps between branches or leaves, free-flying leaves not connected to any branch, spurious geometry, and plant self-collisions in the input configuration. We demonstrate the results using a FEM model reduction simulator that can compute large-deformation dynamics of complex plants at interactive rates, subject to user forces, gravity or randomized wind. We also provide plant fracture (with prespecified patterns), inverse kinematics to easily pose plants, as well as interactive design of plant material properties. We authored and simulated over 100 plants from diverse climates and geographic regions, including broadleaf (deciduous) trees and conifers, bushes and flowers. Our largest simulations involve anatomically realistic adult trees with hundreds of branches and over 100,000 leaves.